Question

Question about vertical/horizontal asymptotes :D

Answer 1

\[f(x)=\frac{ x }{ x-1 }\]

Answer 2

i know x cant equal 1

Answer 3

so there will be an asymptote there

Answer 4

A vertical asymptote exists when the denominator is equal to 0 . So therefore, when x-1 = 0

Answer 5

Good! :D

Answer 6

but my book says there is a vertical and horizontal

Answer 7

y cant equal one, why is that?

Answer 8

If y = 1 then you have a zero in the denominator and yo can't divide by 0.

Answer 9

you mean if x = 1

Answer 10

Yeah x sorry.

Answer 11

The horizontal asymptote is:

\[\lim_{x \rightarrow \infty}\frac{ x }{ x-1}\]

Answer 12

the horizontal is what is killing me

Answer 13

Do you know how to solve infinite limits?

Answer 14

so everything above 1 is cool, but 1 is not

Answer 15

Yeah. Pretty much. Lol.

Answer 16

Because that limit equals 1 . basically It's saying as x gets bigger the y values try to approach 1 but it will never reach there.

Answer 17

so always set up a limit for a fraction function

Answer 18

To find horizontal asymptotes yes.

Answer 19

so if it was

Answer 20

The general formula for an horizontal asymptote is:

\[\lim_{x \rightarrow \infty} f(x)\]

Answer 21

\[\frac{ x }{ x-4 }\]

Answer 22

my vertical and horizontal would be 4

Answer 23

No no.

Answer 24

Your vertical is 4 but your horizontal is 1 because the limit is 1.

Answer 25

Do you know how to find infinite limits?

Answer 26

yes

Answer 27

Okay. The limit as x approaches infinity of that function is 1. Therefore the horizontal asymptote is also 1.

Answer 28

ya i got that one, what about the x/x-4 one?

Answer 29

It's also 1.

Answer 30

You look at the term with the highest degree. In this case it's the x's.

Answer 31

i think i need a refresher on finding limits

Answer 32

Okay. Basically: To find infinite limits, look at the term with the highest power.

Lets say the terms are a and b.